A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Identify the 31st term of an arithmetic sequence where a1 = 26 and a22 = -226. -334 -274 -284 -346

  • This Question is Open
  1. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    hint: we can write these equations: \[\Large \begin{gathered} {a_{22}} = {a_1} + 21d \hfill \\ {a_{31}} = {a_1} + 30d \hfill \\ \end{gathered} \] since the general formula is: \[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\] where d is the constant of your sequence

  2. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    using your data we can rewrite the first equation as follows: \[\Large - 226 = 26 + 21d\] please solve that equation for d

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -252=21d d=-12

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is that right

  5. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that's right!

  6. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    now, substituting that value of d into the second equation, we get: \[\Large {a_{31}} = 26 + 30 \times \left( { - 12} \right) = ...?\]

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -344

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks!

  9. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that's right!

  10. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    :)

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Given the functions f(n ) = 11 and g(n ) = -2(n - 1), combine them to create an arithmetic sequence, an, and solve for the 31st term. an = 11 - 2(n - 1); a31 = -49 an = 11 - 2(n - 1); a31 = -51 an = 11 + 2(n - 1); a31 = 71 an = 11 + 2(n - 1); a31 = 73

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can u help me with this one

  13. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ok!

  14. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    for example, let's consider the first option: we have: \[\Large {a_n} = 11 - 2\left( {n - 1} \right)\] so for n=31, we can rewrite that equationas follows: \[\Large {a_{31}} = 11 - 2 \times \left( {31 - 1} \right) = ...?\] please continue

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a31= -49 right?

  16. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes! that's right!

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain. n an 1 40 2 47 3 54

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can u help me with this one

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Those are the options: an = 40 + 7(n - 1) where n ≥ 40 an = 40 + 7(n - 1) where n ≥ 1 an = 40 - 7(n - 1) where n ≥ 40 an = 40 - 7(n - 1) where n ≥ 1

  21. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Please wait: also the third option is correct, since we can write this: \[\Large {a_{31}} = 11 + 2 \times \left( {31 - 1} \right) = ...?\]

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a31=11+2×(31−1)= 71

  24. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes!

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    71 is not an answer option tho

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh yes it is nevermind

  27. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Which one is the right one? How can I know?

  28. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I'm pondering...

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do I just make a guess?

  30. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    maybe the first one, since the first option contains both f(n) and g(n), whereas the third option contains f(n) and -g(n)

  31. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay thanks!

  32. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    :)

  33. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can u help me with thise one now: Given an arithmetic sequence in the table below, create the explicit formula and list any restrictions to the domain. n an 1 40 2 47 3 54 Those are the options: an = 40 + 7(n - 1) where n ≥ 40 an = 40 + 7(n - 1) where n ≥ 1 an = 40 - 7(n - 1) where n ≥ 40 an = 40 - 7(n - 1) where n ≥ 1

  34. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ok!

  35. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    the constant of your sequence is: \[d = 47 - 40 = 54 - 47 = ...?\]

  36. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    d=7

  37. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    that's right!

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    :)

  39. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so, since the general formula, is: \[\Large {a_n} = {a_1} + \left( {n - 1} \right)d\] replace a_1 with 40 and d with 7, what do you get?

  40. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    an=40+(n−1)7

  41. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    whats in the n spot?

  42. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    n is the number of terms, it is a natural number, more precisely n-1 is the number of terms of the sequence which precede a_n

  43. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay so is the answer the second one

  44. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes! since we start to count from n=1

  45. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    THANKS!

  46. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    :)

  47. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.